It summarizes the precisions and ranges of the different IEEE storage formats. This section describes how floating-point data is stored in memory. The IEEE standard simplifies the task of writing numerically sophisticated, portable programs not only by imposing rigorous requirements on conforming implementations, but also by allowing such implementations to provide refinements and enhancements to the standard itself. IEEE 754 floating-point arithmetic offers users greater control over computation than does any other kind of floating-point arithmetic. The features required by the IEEE standard make it possible to support interval arithmetic, the retrospective diagnosis of anomalies, efficient implementations of standard elementary functions like exp and cos, multiple precision arithmetic, and many other tools that are useful in numerical computation. The IEEE standard also recommends support for user handling of exceptions. Rounding precision for example, if a system delivers results in double extended format, the user should be able to specify that such results are to be rounded to the precision of either the single or double format.Four rounding directions: toward the nearest representable value, with "even" values preferred whenever there are two nearest representable values toward negative infinity (down) toward positive infinity (up) and toward 0 (chop).The five types of floating-point exceptions are invalid operation, division by zero, overflow, underflow, and inexact. Five types of IEEE floating-point exceptions, and the conditions for indicating to the user the occurrence of exceptions of these types.For operands not lying within the specified ranges, these conversions must produce results that differ from the exact result by no more than a specified tolerance that depends on the rounding mode. For operands lying within specified ranges, these conversions must produce exact results, if possible, or minimally modify such exact results in accordance with the rules of the prescribed rounding modes.
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